
By modeling landscape regions as random networks, we will show in a forthcoming paper [1]} that the uniform-time probabilities (REF ) favor regions that are close to the
directed percolation phase transition [2]}. Thus landscape dynamics belong to the universality class of directed percolation — the paradigmatic non-equilibrium critical phenomenon. As usual, the
predictive power of criticality lies in scale invariant observables characterized by critical exponents. We will argue that the probability distribution for the CC is a power-law,
that favors a naturally small and positive vacuum energy. Tantalizingly, this hints at a deep connection between non-equilibrium critical phenomena on the landscape and the near-criticality of our universe.

The connection with protein folding funnels deserves further exploration. The problem of search optimization on complex, high-dimensional energy landscapes has already been solved by naturally-occurring proteins. A fascinating result in protein folding is that conformation networks share many properties of real-world networks [3]}: their degree distribution is scale-free, they enjoy the small-world property, and they are hierarchical. It will be interesting to study the implications of similar properties holding in regions of the string landscape.

